Title:

Density diagnostics and inhomogeneous nonisothermal plasmas

Many astrophysical plasmas, such as are found in the sun, nebulae and, supernova remnants etc are often analysed spectroscopically assuming in a first approximation that they are homogeneous in nature. However, when several different diagnostics are applied, different plasma parameters, e. g. electron density and temperature, are usually inferred from each diagnostic. This is consistent with imaged observations of the solar atmosphere, for instance, which show that it is, in fact, highly inhomogeneous, and of nonisothermal structure, so that a range of temperatures and densities contribute to the line intensities used in the spectroscopy. Such inhomogeneity can severely affect accurate determination of plasma parameters, such as electron densities. In this thesis, Chapters 1 and 2 are designed to introduce and review the relevant topics considered in the later Chapters. Chapter 1 considers the use of solar plasma spectroscopy for the determination of the electron temperature and density in the solar atmosphere, discussing the different techniques developed for this purpose. Our discussion is restricted to plasma diagnostics inferred from the high temperature solar spectrum, which produces lines mainly in the UV, EUV, and Xray regions of the electromagnetic spectrum. The necessary atomic physics involved, which is closely related to solar physics diagnostics, is also discussed in detail. In Chapter 2 we review the present status of observational knowledge of the solar atmosphere at UV, EUV and Xray wavelengths, paying special attention to plasma electron density inhomogeneities. The main body of this thesis is contained in Chapters 36. In Chapter 3, we present a simple, but accurate, analytical, representation which describes line ratios as a function of electron density. This representation is found to lead to an extremely good representation of actual line ratio curves, obtained by numerical methods that require much theoretical effort and very accurate atomic data. This representation is shown to be an excellent method for electron density determination in solar plasmas, and to provide a more flexible treatment of the effect of plasma inhomogeneities on density sensitive line ratios. Chapter 4 discusses the problem of interpreting density sensitive line strengths from an isothermal plasma of inhomogeneous density. We show that the problem can be expressed in terms of deriving an emission measure function zeta(ne) per unit density from a set of line strengths and that any particular line ratio yields a spectroscopic 'mean density' (ne). The value of (ne) will differ for different line pairs, and differ from both the volumetric mean n and emissivity mean n unless the plasma is homogeneous. For a single line ratio and total emission measure, the homogeneous solution ne(r)=(ne) yields the minimum possible plasma volume which is found to fall below the true plasma volume to an extent which increases with the inhomogeneity of the real plasma. This result, explains, in terms of plasma inhomogeneity, the small filling factors commonly found when emitting volumes, inferred using (ne) together with the total emission measure, are compared with spatially resolved total volumes. In Chapter 5 the problem of interpreting densities in inhomogeneous nonisothermal plasmas from density sensitive line ratios is discussed. It is shown how the concepts of emission measure differential in density zeta(ne) and emission measure differential in temperature xi(T) can be generalised to analyse arbitrary plasmas. In Chapter 6 we discuss another reason for deducing incorrect electron densities in the solar atmosphere, namely the noise in the observed line intensities and in the atomic data. The resultant bias in the estimated densities, as well as the confidence interval, is determined for some examples. A fairly brief discussion is given of how the noise on line ratios can affect the estimated densities and, therefore, the required accuracy for obtaining reasonable values of ne. Finally, Chapter 7 discusses possible future work inspired by, or related to, the considerations of this thesis. In particular, the investigation of the effect of the plasma inhomogeneity on different models of the solar atmosphere as well as on different solar phenomena is considered. In addition, the effect of noise on the different atomic parameters present in our representation (Chapter 3), and a comparison with that of the line ratio's are shown to be important.
